The question to Mr Trump, the front-runner in the 2016 Republican campaign, came at a town hall in Rochester, New Hampshire.

The first person the billionaire property mogul called on said: "We have a problem in this country. It's called Muslims."

"We know our current president is one," the man said of Mr Obama, who is Christian. "You know he's not even an American."

Mr Trump, a driver of the "birther" movement that falsely claimed Mr Obama was born outside the US, first responded with feigned exasperation, saying "we need the question," to laughs, before letting the man continue.

"We have training camps growing where they want to kill us. That's my question," the audience member continued. "When can we get rid of it?"

Mr Trump did not dispute the assertion that militants operate training camps on American soil and said he had heard others raise the issue.

"We're going to be looking at a lot of different things. And you know, a lot of people are saying that, and a lot of people are saying that bad things are happening out there," said Mr Trump.